Based on the analysis of non-verbal inter-human interaction, this paper proposes a model for estimating human friendships in the presence of a humanoid robot. Our previous study in an elementary school provided rich video data of two months of inter-human interaction in the presence of a humanoid robot. Such data are particularly useful for developing a robot's social ability: a friendship estimation capability. We analyzed the video based on an observation method to analyze the interaction among children and the robot. From their non-verbal interactions, several important factors for friendship estimation were retrieved, including touch, gaze, co-presence, and distance. Gender was also considered a factor in the model, since gender differences were observed in non-verbal interactions. The model discriminated between friendly and non-friendly relationships among the children with 74.5% accuracy for boys and 83.8% for girls.